introduction to nuclear fusion - snu open courseware fusion1.pdffusion in nature nobel prize in...
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Introduction to Nuclear Fusion
Prof. Dr. Yong-Su Na
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2
What is nuclear fusion?
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Matter and Energy
• Chemical reactions (combustion)
heating
fuels
reaction energy
products
Eout
Mout
Ein
Min
Matter-EnergyTransformation
reactor/generator
eVOHOH 32
1222 +→+
KKJ
JeV 11600
/1038.1
106.1 1
23
19
=
=
−
−
eVKT 1=
4
Matter and Energy
• Chemical reactions (combustion)• Fission process• Fusion process
• Total energy conservation including rest mass energy
• If Δm = Mout-Min < 0, then we can get Eout > Ein
outoutinin MEME +→+
heating
fuels
reaction energy
products
Eout
Mout
Ein
Min
Matter-EnergyTransformation
reactor/generator
http://www.meteoweb.eu/2011/09/e-possibile-superare-la-velocita-della-luce-teoria-della-relativita-a-rischio/88437/, Dec, 2014
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Mass Defect Energy of Nuclear Reaction
edba +→+reactants products
**
afterbefore EE =
)()()()( 2
,
2
,
2
,
2
, cmEcmEcmEcmE eekddkbbkaak +++=+++
Total energy
( ) ( ) ekdkedba EEcmcmcmcm ,,
2222 ++++
)()( baedab mmmmm +−+=
abbkak QEE + ,,For
( ) ( ) 2
2
)( cm
cmmmmQ
ab
edbaab
−=
+−+=
22
,,2
1
2
1eeddekdkab vmvmEEQ +=+
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Mass Defect Energy of Nuclear Reaction
22
,,2
1
2
1eeddekdkab vmvmEEQ +=+
eedd vmvm =
ab
ed
dekab
ed
edk Q
mm
mEQ
mm
mE
+
+ ,, ,
Momentum conservation for reactions with CM at rest
Ex) d-t fusion reaction +→+ ntd
MeV 6.17=dtQ
kgm
kgm
mm
n
p
pn
27
27
10674927.1
10672621.1
−
−
=
=
+
+=
+
+=
+
+=
22
2
22
222
22
2
1
2
1
2
1
2
1
2
1
2
1
dde
d
e
e
d
ed
e
ddd
e
d
ed
e
dd
e
ed
ed
edd
vmvm
m
m
m
mm
m
vmvm
m
mm
m
vmm
mm
mm
mvm
Derive!
MeV 5.35
1 ,MeV 14.1
5
4,, dtkdtnk QEQE
eVOHOH 32
1222 +→+
Fusion in Nature
• Nuclei are made up of protons and neutron, but the mass of a nucleusis always less than the sum of the individual masses of the protons and neutrons which constitute it.
• Binding energy: the amount of energy released when a particular nucleus is formed.
..)( EBXnZAZp A
Z +→−+
22)])([(.. mccmZAZmmEB npX −=−−−−
Δm < 0: released energy (exothermic or exoergic)
http://www.daviddarling.info/encyclopedia/B/binding_energy.html
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Fusion in Nature
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Sun producing 3.8x1026 J/s
equivalent to 4.3x109 kg
Sun composed of proton (73%),
He (25%), etc
How old is the sun?
How long is the sun’s lifetime?
Fusion in Nature
Nobel prize in physics 1967“for his contribution to the theory of nuclear reactions, especially his discoveries concerning the energy production in stars”
Hans Albrecht Bethe(1906. 7. 2 – 2005. 3. 6)
• Fusion reactions by which stars convert hydrogen to helium
- The PP (proton-proton) chain: in stars the mass of the Sun and less
- The CNO cycle (Bethe-Weizsäcker-cycle): in more massive stars
http://www.nobelprize.org/nobel_prizes/physics/laureates/1967/bethe-bio.html 9
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Fusion in Nature
One of the most impressive discoveries was the origin of the stars, that makes them continue to burn. One of the men who discovered this was out with his girl friend the night after he realized that nuclear reactions must be going on in the stars in order to make them shine. She said “Look at how pretty the stars shine!” He said “Yes, and right now I am the only man in the world who knows why they shine.” She merely laughed at him. She was not impressed with being out with the only man who, at that moment, knew why stars shine. Well, it is sad to be alone, but that is the way it is in this world.
- The Feynman Lectures on Physics I, p.3-7
• Fusion reactions by which stars convert hydrogen to helium
- The PP (proton-proton) chain: in stars the mass of the Sun and less
- The CNO cycle (Bethe-Weizsäcker-cycle): in more massive stars
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Fusion in Nature
• The PP (Proton-Proton) Chain
Step 1: Smash two protons together to make deuterium
MeVdpp 2.1+++→+ +
Positron: antiparticle of the electron-like an electron with charge of +1eNeutrino: electrically neutral, weakly interacting elementary subatomic particle
http://burro.astr.cwru.edu/Academics/Astr221/StarPhys/ppchain.html
MeVnp 782.0−++→ +
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Fusion in Nature
• The PP (Proton-Proton) Chain
Gamma ray: electromagnetic radiation of an extremely high frequency (very high energy photon)
MeVHedp 5.53 ++→+
Do Steps 1 and 2 again so to have two 3He nuclei.
Step 2: A proton crashes into a deuterium nucleus, making 3He
http://burro.astr.cwru.edu/Academics/Astr221/StarPhys/ppchain.html
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Fusion in Nature
• The PP (Proton-Proton) Chain
MeVpHeHeHe 9.122433 ++→+
Step 3: Mash two helium-3 nuclei together to make helium-4
http://burro.astr.cwru.edu/Academics/Astr221/StarPhys/ppchain.html
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Fusion in Nature
MeVdpp 2.1+++→+ +
MeVHedp 5.53 ++→+
MeVpHeHeHe 9.122433 ++→+
+→+ BeHeHe 743
+→+ − LiBe 77
nucleosynthesis
PPII Chain (14-23x106 K)
HeHepLi 447 +→+
PPIII Chain ( > 23x106 K)
+→+ BpBe 87
++→ +BeB 88
HeHeBe 448 +→
• The PP (Proton-Proton) Chain
http://csep10.phys.utk.edu/astr162/lect/energy/ppchain.html
10-14x106 K
CX → years
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Fusion in Nature
- Most of 4He nuclei being produced in the Sun are
born in the PP chain (98.3%).
K61015TSun
• The PP (Proton-Proton) Chain
http://www.nasa.gov/mission_pages/galex/20070815/f.html
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Fusion in Nature
MeVNpC 9.11312 +→+
MeVCN 5.11313 +++→ +
MeVNpC 6.71413 +→+
MeVOpN 3.71514 +→+
MeVNO 8.11515 +++→ +
MeVCpN 0.51215 ++→+
MeVp 1.25224 +++→ +
• The CNO Cycle
KTstar
61013
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Fusion in Nature
keVBe 928 −→+
MeVCBe 367.7128 ++→+
• The triple alpha process
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Fusion in Nature
http://jcconwell.wordpress.com/2009/07/20/formation-of-the-elements/http://eqseis.geosc.psu.edu/~cammon/HTML/Classes/IntroQuakes/Notes/earth_origin_lecture.html
Layers of Fusion in the final stage of a massive star
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Fusion reaction
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Physical Characterization of Fusion Reaction
rr
qqF ba
ac 3
0
,4
1
=
a b
rr
mmGF ba
ag 3, −=
• The electrostatic force caused by positively charged nuclei is very strong over long distances, but at short distances the nuclear force is stronger.
• As such, the main technical difficulty for fusion is getting the nuclei close enough to fuse.
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Physical Characterization of Fusion Reaction
( ) ( ) mRAARR
ptdR
qqRU
pbap
ba
153/13/1
0
00
0
107.13.1 ,
, ,for MeV 4.0~4
1)(
−−=+
=
]exp[1
)Pr(r
ba
r v
vtunneling −
Reflection and tunneling of an electron wave packet directed at a potential barrier
A. B. Balantekin and N. Takigawa, 'Quantum tunneling in nuclear fusion', Rev. Mod. Phys. 70, 77 (1998).
0VE
( )
aek
k
akk
kT
2
2
2
0
2
0
222
0
22
0
2
02
4
sinh)/2(
)/2(
−
+
++=
0
Attractive strong nuclear force
Sun: 1.4 keV
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Physical Characterization of Fusion Reaction
• By 1928, George Gamow had solved the theory of the alpha decay of a nucleus via tunneling. After attending a seminar by Gamow, Max Born recognized the generality of quantum-mechanical tunneling.
(Max Born, Nobel Prize in Physics 1954)
Max Born (1882-1970)
George Gamow(1904-1968)
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Fusion Reaction Cross Sections
- Fusion cross section for low energy
ECM < U(R0) by quantum mechanical
tunneling process:
EB
ab eE
AE /)( −= Gamow theory
(1938)
0
22/12/1 /2 ., heZZmBconstA bar
−==
228224 10101 mcmbarn −− ==
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Fusion Reaction Rate Parameter (Reactivity)
• Fusion reaction rate density
abrbafu vNNR =
( ) babbaaba
v v
baabab vdvdvFvFvvvvv
a b
33)()(
−−=
• σ-v parameter
rbafu vNNR bar vvv
−=
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Fusion Reaction Rate Parameter (Reactivity)
- Thermodynamic equilibrium- Both species at the sametemperatures
http://www.scienceall.com/jspJavaPopUp.do?classid=CS000140&articleid=611&bbsid=146&popissue=java
)()( xxxx vMvF →
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Fusion Reaction Rate Parameter (Reactivity)
• Fusion reaction rate density
abrbafu vNNR =
fuabbafufufu QvNNQRP ==
• Fusion power density
( ) babbaaba
v v
baabab vdvdvFvFvvvvv
a b
33)()(
−−=
• σ-v parameter
rbafu vNNR bar vvv
−=